1) Willpower alone (again, in the vain of Fairy Tail), or...
2) The use of an ability/skill acquired off-screen, or lastly by...
3) A last-second power-up (otherwise known as an 'ass-pull')
However, the story is very cohesively structured and develops at just the right pace. Also, every character, from the MC to everyone in the main supporting roster are able to nicely fit into the story, all the while being fully 'individualized', with no boring or non-essential characters among those mentioned. The music is also highly unique and fitting for this series, meshing well with the style and tone of its artwork and the series' general feel. The 'level-up' aspect is also very prominent and well executed.
The MC, Allen Walker, is another plus of this show. He might not be Mr. Buff-Mcbruteforce like Guts from Berserk, nor does he fit the mold of a suave anti-hero type, but he at very least doesn't have the take-shit-lying-down personality of a Harem protagonist or the neanderthal-like, tantrum-throwing character exemplified by Xin from Kingdom and Natsu from Fairy Tail. Instead I'd say that Allen is gentle without being a spaz, crafty/cheeky without entering into straight-up anti-hero territory, as well as strong while at the same time not being a retard. All-in-all, a quite tolerable, well-rounded MC that one can easily sympathize with and root for.
I'll conclude by simply saying that I view D.Gray-man as the best 'Power-up" anime there is. So if that's a genre you're into then this series is bound to be up your alley.
